An observer moving at a speed of 0.990 c relative to a rod (Fig. P26.14) measure
ID: 2240579 • Letter: A
Question
An observer moving at a speed of 0.990 c relative to a rod (Fig. P26.14) measures its length to be 2.00 m and sees its length to be oriented at 30.0 o with respect to the direction of motion. What is the proper length of the rod?
b)What is the orientation angle in a reference frame moving with the rod?
An observer moving at a speed of 0.990 c relative to a rod (Fig. P26.14) measures its length to be 2.00 m and sees its length to be oriented at 30.0 o with respect to the direction of motion. What is the proper length of the rod? What is the orientation angle in a reference frame moving with the rod?Explanation / Answer
As we know that
L' = L0*sqrt(1 - v^2/c^2)
Along the Direction of motion of Observer
L' = 2*Cos30
= 1.732 m
Therefore
1.732 = L0*sqrt(1 - 0.99^2)
L0 = 12.2778 m
Perpendicualr the Direction of Motion , Length remains Unchanged = 2*Sin30
= 1 m
Therefore
Propoer Length = sqrt(1^2 + 12.2778^2)
= 12.318 m
Orintation Angle = arctan(1/12.2778)
= 4.656 degree